changing the stock power and ground wire to the battery

i was reading up on stereo installation and felt stupid that i didn't realize on my own that i should be running a new ground from the battery to the cars fram the same gauge as the power wire i'm running off of it
so i was looking at battery terminals to make a clean install for all of this and got to wondering what gauge wire is currently going to my battery from the alternator
i checked and it's 3awg
i was wondering if it would be a good or a bad idea to run either 2 or 1/0 gauge between the alternator and the battery and the same to ground the battery?
if i did do this i was just planning on using stereo power wire, would that be acceptable as well?


thanks
Sean